Nonlinear Dynamics

, Volume 88, Issue 4, pp 2491–2501 | Cite as

Evoking complex neuronal networks by stimulating a single neuron

  • Mengjiao Chen
  • Yafeng Wang
  • Hengtong Wang
  • Wei Ren
  • Xingang Wang
Original Paper
  • 216 Downloads

Abstract

The responses of electrically coupled neuronal network to external stimulus injected on a single neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus increases, the network will be transiting from the resting to firing states and then restoring to the resting state, thereby showing a bounded firing region in the parameter space. Furthermore, it is found that as the coupling strength among the neurons decreases, the firing region is gradually expanded and, at the weak couplings, it could be separated into several disconnected subregions. By a simplified network model, we conduct a detailed analysis on the bifurcation diagram of the network dynamics in the two-dimensional parameter space spanned by stimulating intensity and coupling strength, and, by introducing a new coefficient named effective stimulus, explore the underlying mechanisms for the modified firing region. It is revealed that the coupling strength and stimulating intensity are equally important in evoking the network, but with different mechanisms. Specifically, the effective stimuli are shifted up globally by increasing the stimulating intensity, while are drawn closer by increasing the coupling strength. The dynamical responses of small-world and random complex networks to external stimulus are also investigated, which confirm the generality of the observed phenomena. The findings shed new lights on the collective behaviors of complex neuronal networks and might help our understandings on the recent experimental results.

Keywords

Complex neuronal network Coupled oscillators Excitability Bifurcations 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China under the Grant No. 11375109, and by the Fundamental Research Funds for the Central Universities under the Grant Nos. GK201601001 and GK20150-3027.

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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Mengjiao Chen
    • 1
  • Yafeng Wang
    • 1
  • Hengtong Wang
    • 1
  • Wei Ren
    • 2
  • Xingang Wang
    • 1
  1. 1.School of Physics and Information TechnologyShaanxi Normal UniversityXi’anChina
  2. 2.College of Life Science, Key Laboratory of MOE for Modern Teaching TechnologyShaanxi Normal UniversityXi’anChina

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